Process level moderate deviations for stabilizing functionals

2006/03/16 by Eichelsbacher, Peter, Schreiber, Tomasz
#60D05 #60F05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.math/0603402

Abstract

Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. In this paper we prove process level moderate deviation principles (MDP) for such functionals, which are a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including random sequential packing, birth-growth models, germ-grain models and nearest neighbor graphs.

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